Recent exhaust gas regulation requires exhaust systems of vehicle engines to monitor control conditions of exhaust gas by means of in-vehicle computers. An example of an item to be monitored may include a deterioration condition of a catalyst which purifies exhaust gas (see JP-A-2003-206784). In JP-A-2003-206784, oxygen sensors are provided before and behind the catalyst respectively, and determination as to whether the catalyst is deteriorated or not can be made based on output values of these two oxygen sensors.
Specifically, numbers of times of output inversion between a rich state and a lean state in the two oxygen sensors can be used. For example, when the catalyst is normal to adsorb oxygen sufficiently, the number of times of output inversion in the downstream oxygen sensor approaches zero. Therefore, a ratio of the number of times of output inversion in the upstream oxygen sensor to that in the downstream oxygen sensor increases. On the other hand, when the catalyst is deteriorated so that an oxygen adsorbing capability of the catalyst is lowered, the number of times of output inversion in the downstream oxygen sensor approaches the number of times of output inversion in the upstream oxygen sensor. Therefore, the ratio of the number of times of output inversion in the upstream oxygen sensor to that in the downstream oxygen sensor decreases. Thus, it is possible to determine that the catalyst is deteriorated when the aforementioned ratio is lower than a predetermined value.